I think Browsers on Windows sometimes do dirty tricks and already load on boot (in the background). So once you click to "open" the browser, it's already in memory and pops up instantly. That might be the reason why it's instand on Windows, and takes time on Linux.
Both my browsers on Linux also take 2-3s to open. Though I regularly don't notice. I'll just leave the browser open all day, because I need it all the time. I closed and re-opened it right now, and it definitely also takes a very few seconds on my machine with a GNOME desktop.